The Venn diagram below shows the 8 students in Mr. Parker's class. The diagram shows the memberships for the Volleyball Club and the Spanish Club. Volleyball Spanish Note that "Austin" is outside the circles since he is not a member of either club. One student from the class is randomly selected. Keith Let A denote the event "the student is in the Volleyball Club." Let B denote the event "the student is in the Spanish Club." Jose Keiko Mai Felipe Lisa Answer each part below. If necessary, consult a list of formulas. Lamar Austin (a) Find the probabilities of the events below. Write each answer as a single fraction. P(4) = 0 P(B) = ] P(4 and B) = ] P(4 or B) = | P(4) + P(B) – P(4 and B) = ] (b) Select the probability that is equal to P(A) +P(B) - P(A and B). O P (A) O P (A and B) O P(A or B) O P(B)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
The Venn diagram below shows the 8 students in Mr. Parker’s class. The diagram shows the memberships for the Volleyball Club and the Spanish Club.

Note that "Austin" is outside the circles since he is not a member of either club.

One student from the class is randomly selected.
Let \( A \) denote the event "the student is in the Volleyball Club."
Let \( B \) denote the event "the student is in the Spanish Club."

Answer each part below. If necessary, consult a list of formulas.

**Venn Diagram Explanation:**
- **Volleyball Club**: Circle on the left with members: Mai, Jose, Felipe
- **Spanish Club**: Circle on the right with members: Jose, Felipe, Keith, Keiko, Lisa, Lamar
- **Overlap (Both Clubs)**: Jose, Felipe
- **Outside Both Circles**: Austin

**Task (a):** Find the probabilities of the events below. Write each answer as a single fraction.

- \( P(A) = \) \(\_\)
- \( P(B) = \) \(\_\)
- \( P(A \text{ and } B) = \) \(\_\)
- \( P(A \text{ or } B) = \) \(\_\)
- \( P(A) + P(B) - P(A \text{ and } B) = \) \(\_\)

**Task (b):** Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \).

- \( \circ P(A) \)
- \( \circ P(A \text{ and } B) \)
- \( \circ P(A \text{ or } B) \)
- \( \circ P(B) \)
Transcribed Image Text:The Venn diagram below shows the 8 students in Mr. Parker’s class. The diagram shows the memberships for the Volleyball Club and the Spanish Club. Note that "Austin" is outside the circles since he is not a member of either club. One student from the class is randomly selected. Let \( A \) denote the event "the student is in the Volleyball Club." Let \( B \) denote the event "the student is in the Spanish Club." Answer each part below. If necessary, consult a list of formulas. **Venn Diagram Explanation:** - **Volleyball Club**: Circle on the left with members: Mai, Jose, Felipe - **Spanish Club**: Circle on the right with members: Jose, Felipe, Keith, Keiko, Lisa, Lamar - **Overlap (Both Clubs)**: Jose, Felipe - **Outside Both Circles**: Austin **Task (a):** Find the probabilities of the events below. Write each answer as a single fraction. - \( P(A) = \) \(\_\) - \( P(B) = \) \(\_\) - \( P(A \text{ and } B) = \) \(\_\) - \( P(A \text{ or } B) = \) \(\_\) - \( P(A) + P(B) - P(A \text{ and } B) = \) \(\_\) **Task (b):** Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \). - \( \circ P(A) \) - \( \circ P(A \text{ and } B) \) - \( \circ P(A \text{ or } B) \) - \( \circ P(B) \)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman